Question

In a​ state's Pick 3 lottery​ game, you pay ​$1.37 to select a sequence of three digits​ (from 0 to​ 9), such as

755. If you select the same sequence of three digits that are​ drawn, you win and collect

​$281.04.

Complete parts​ (a) through​ (e).

a. How many different selections are​ possible?

b. What is the probability of​ winning?

​(Type an integer or a​ decimal.)

c. If you​ win, what is your net​ profit?

​(Type an integer or a​ decimal.)

d. Find the expected value.

​(Round to the nearest hundredth as​ needed.)

e. If you bet $1.37 in a certain​ state's Pick 4​ game, the expected value is −$1.09.

Which bet is​ better, a ​$1.37 bet in the Pick 3 game or a $1.37 bet in the Pick 4​ game? Explain.

A. The Pick 4 game is a better bet because it has a larger expected value.

or

B. Neither bet is better because both games have the same expected value.

Answer 1

Answer:

a)

Each of the 3 digits can be any amongst 0 to 9 i.e. any of these 10 digits.

So, the total number of different selections possible = (10)(10)(10) = 1000

b)

Since only one sequence can be the winning sequence, so

P(winning) = 1/1000 = 0.001

c)

Net profit = 281.04 - 1.37 = $279.67

d)

Expected value = 281.04*(0.001) + (-1.37)*(1-0.001)

= -1.08759

e)

Since the expected value in both games is equal, so, neither game is better.

Hence option B is the correct option.

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